I will admit to being a bit of a dummy and find the hyper cube a bit of a challenge.

If we took something a bit easier, say a line.

What would a 10 metre four structural dimension line look like?

Co-ordinates w, x, y, z to w1, x1, y1, z1
where w is a number in the four dimension.

So for us a line is y = mx + b where m is gradient and b is offset.
Lets assume z = 0 for ease.
Could w = 1 metre and still be a line to us?

Cheers Mike

Maybe if we start in two dimensions and work up then.

We have a 2D character Dan.
He is a flatlander.

Line A,B is 10 metres.
So y = mx + b where x = 0 to 10 metres
m = 0 and b = 0
Therefore it is a line on the x axis for 10 metres only from 0 to 10.

In co-ordinates he sees only x and y but not z.
So for z = 1 means means nothing to Dan.
He still sees only the line from the side x(0), y(0) to x(10), y(0)

Dan can not see he is displaced from his line by a distance of 1 metre in the z direction.
He may see there are two solutions as he passes through the line.
There is a line that fits his world at A(0,0,1) to B(10,0,1)
and a line also at A(0,0,-1) to B(10,0,-1)

He would of course not see the z co-ordinate but would regard it as two lines.

This is the light source bit.
What if all the light in his world came from the edges of his plane.
Outside a distance of z = 1 he is bathed in light from one side.
Inside a distance of z = 1 he receives less light from the edges.

Say he is at x = 5.
His light is from the ends and any local source of light he brought with him.

How does this sound? Am I on the right track here?

Cheers Mike

For goodness sake. Draw a picture.

A __________________________________________________ ____ B


We can not see what you are talking about.

Great idea does this help



I was looking at this and my math is mistaken and a painfully obvoius mistake.

Dan's world is experiencing two lines A(0,1,1) to B(10,1,1)
and the second line A(0,-1,1) to B(10,-1,1)

The z dimension is one he can't experience.
His world wraps over the tube that exist on the x axis.

The point being if he was on the outside of the plane he would be bathed in all the light from our three dimensional world and it would be exceptionally bright.

If however the wrap around the tube that is on the x axis had him on the inside his world would be incredibly dark with only light coming in from the ends of the tube and of course from the line of the plane he is on.

The difference is whether he is in or outside of what he could only experience as a worm hole in his two dimensional world.

Cheers Mike

The reason



I try to understand thing by the way they are different.
For instance I have a holden and a volvo.

If I tried to identify them by the way they are the same it would be very hard.
They both have for wheels and an engine and windows and so on.

The holden is a different colour and has a longer looking shape.
The volvo looks "boxy" (well it is a volvo) and has much better paintwork.

If our Dan had his plane go over the inflated third dimension he would have all the light of the three dimensions flood onto him.



If he travels through the inside of inflated tube part of his world his light can only come from his two dimensional world and so is much darker.



He could not possibly know he was on the inside unless he could "see" far enough to planes that cross his at an angle and deduce by their shape that he is in a bend of his dimension.

When talking of worm holes the obvious assumption is that we are always of course on the outside of it. What if we we on the inside? Would that then mean we in three dimensions could not be bathed in the full light of four dimensions if we were on the inside of a worm hole.

We exist in a four dimensional expansion of space time and so should be receiving all the light of that four dimensions if we were on the outside of the worm hole. But like Dan is it possible that our experience of light is limited to only what can come through our three dimensions because we are also on the inside.

It is like when the flow of electricity was made. There was a 50% chance we would pick which way the electrons would flow. Observations made later and better measurements made it clear we had to reverse the flow idea and the electron flows from negative to positive.

Cheers Mike

One little detail I would like to add to your OP, Michael Noonan. I should point out that the following may be very wrong.

First, this is what we've got so far:

(x0,y10,z0).............(x10,y10,z0)
C_____________________D
..l.................................l
..l.................................l
..l.................................l
..l.................................l
..l.................................l
Al_____________________lB
(x0,y0,z0).................(x10,y0,z0)

If this plane were to be shifted 1 unit in the z direction, it is indeed true that Dan would not notice anything, as his existence is purely 2D (in the ABCD plane). Furthermore, I doubt that it is even possible for Dan to measure any shift in the above situation.

However, if the situation looked something like this:


........C^
.........l...\.(x10,y10,z0).......(x10,y10,z10)
.........l.....\D________________E
.........l......l..........................l
.......Al......l..........................l
..........\....l..........................l
............\..l..........................l
..............\B________________F
..........(x10,y0,z0)...........(x10,y0,z10)

In this situation, I believe that Dan would be able to move from A to B, for instance, and then from B to F. This is because the three dimentions are not something that is rigid. That is to say, that once Dan reaches point B (coming from A), he will see and think that he is still in the two dimentions he knows, except his world is now 10x20, instead of 10x10. So Dan's 2D world almost "rotates" as he passes B, but never loses its 2D-ness (Dan would not notice the "rotation"). Once Dan passes B, and his world "rotates", the relative third dimention is now in a different direction for him, as it appears to us (3D people), but from Dans, perspective, if he wanted to move in the third dimention, he would still have to use the same method for moving from the AB stretch, as moving from the BF stretch.

Notice, however, that the dimentions are connected, if they werent, things would be different. For instance, if the chunk (x10,y0,z0) to (x10,y0,z1) was missing everywhere on the y axis, then Dan would have no way of travelling past point B. The plane in the Z dimention would exist for Dan to walk on IF he could somehow get there, but there is no physical connection that Dan can use to get there, so hes stuck on the ABCD plane.

Dan would also not be able to get to the plane in the Z direction if the situation looked like this:

........C^
.........l...\
.........l.....\D________________E
.........l......l..........................l
.......Al......l..........................l
..........\....l..........................l
............\..l..........................l
..............\B________________F
................\...........
..................\.........
.................B1\
...............(x20,y0,z0)

In this situation, Dan would ony see his xy plane, and not the yz one. For him, the above world would look identical to the previous example. It would be a 10x20 2D world.

Now lets move to the slightly harder 4D scenario.

Notice how when extruding from a line to a plane, the extrusion is one-dimentional, meaning, we take the line, and "move" it upward, filling all the created space in between. When extruding a plane into a cube, the extrusion is 2D, meaning, we take the 2D plane, and extend that 2D-ness "into" the third dimention, filling the now 3D space. When we have a cube, we have to do the same, meaning, we take all of the sides and make another extrusion, keeping all the points attached. This time the extrusion is going to be 3D, creating the 4th dimention. Here is a fairly common image of one.

Im not sure about this one, but I think that in a 4D cube, the space around the 3D cube, is the 4th dimention, allowing the 3D cube "inside" to move in the additional third dimention, allowing for the most useful illusion/concept of time (don't burn me for this one ). The whole thing is still one object though.

As you can see, 4D is nothing special, what you want is the fifth dimention!

Finally, remember how in the last illustration Dan could not move to point F, becasue his 2D plane extended past the point where the two planes intersected? Dan couldn't go "through" his 2D world to jump to the other plane, forcing him to continue along the x axis towards B1. Also, remember how in the second illustration Dan WAS able to move to the other dimention, becasue his "original" dimention "ended" (mind you, for Dan, there is no distinction between scenario 2 and 3, the difference is only noticeable for us higher dimentional beings)

In any case, the point is that if you continue going in one direction for a very long time, and if this dimention is finite (or when 0.9999...finally becomes 1 ), then if you reach that "end" - THAT is when our world will "rotate" in the eyes of higher dimentional beings, but the rotation will not be noticeable to us, much like in the example with Dan.

I really hope I got this right. Please correct me if I didn't.


Thanks.

Thank you for that now it certainly looks better afterburner.

Dan could not cut across from one side to the other in the line of his plane.

It would be an unnoticed interuption of his existence where his plane was bent into our 3D world. His perception of it would be as a plane and he would not notice the bend out of his line.

To him everything would still look like straight lines and his experience of his dimensions would be two structural and one time say the time it took to walk from x = 5 in his world to x = 6.

Cheers Mike